How to find marginal revenue. Marginal income and its importance in making managerial decisions Marginal income is equal to

The relationship of fig. 7.3 and 7.4 is as follows: after gross income reaches its maximum, marginal income becomes negative. This pattern will help us later to understand at what part of the demand curve the monopolist sets a profit-maximizing price. Note also that in the case of a linear demand curve D, the schedule MR crosses the x-axis exactly in the middle of the distance between zero and the demand at zero price.

Let us return to the costs of the firm. We know that the average cost (AU) have at first, when the number of units of production is increased

Chapter 7

appears to be a decreasing trend. Later, however, when a certain level of output is reached and exceeded, average costs begin to rise. The dynamics of average costs, as we know, has the form (L-shaped curve (see Chapter 6, § 1). Let us depict the dynamics of the average, total (gross) and marginal costs of an imperfect competitor firm on an abstract digital example. But first, we recall once again the following designations:

TC=QxAC,(1)

i.e., gross costs are equal to the product of the quantity of goods and average costs;

MS= TS p - TS pA, (2)

i.e., marginal cost is equal to the difference between the gross cost of n units of the good and the gross cost of n-1 units of the good;

TR=QxP,(3)

i.e., gross income is equal to the product of the quantity of goods and its price;

MR= TR n - TR n .,, (4)

i.e. marginal revenue is equal to the difference between the gross revenue from the sale of n units of the product and the gross revenue from the sale of n-1 units of the product.

Columns 2, 3, 4 (Table 7.3) characterize the production conditions of the monopoly firm, and columns 5, 6, 7 - the conditions of sale.

Let us once again return to the concept of perfect competition and the equilibrium of the firm in these conditions. As you know, equilibrium occurs when MS\u003d P, and the price in conditions of perfect competition coincides with marginal revenue, therefore, we can write: MS = MR = R. For a firm to achieve full equilibrium, two conditions must be met:

1. Marginal revenue must equal marginal cost;

2. Price must equal average cost. 1 And this means:

MC=MR=P=AC 5)

sheet will be exactly the same determined

dynamics of marginal revenue (MR) and

marginal cost (MC). Why ? By-

because each additional

unit, product price adds

some amount to gross income

and at the same time -

Table 7.3 Col and ches t in t ovarov, in and dy costs, price and in and types of income

to gross costs. These are some quantities marginal revenue and marginal costs. The firm must constantly compare these two values. While the difference between MR and MS positive, the firm is expanding its production. You can draw the following analogy: as the potential difference provides the movement of electric current, so the positive difference MR and MS allows the firm to expand its output. When MR= MS, comes "peace", the equilibrium of the firm. But what price will be established in this case under "conditions of imperfect con-

Chapter 7

Market mechanism of imperfect competition

smoking? What will be the average cost (AS)"? Will the formula be followed? MS - MR = P = AC?

Let's turn to Table. 7.3. The monopolist, of course, seeks to set high unit prices. However, if he sets the price at $41, he will sell only one unit of the product, and his gross income will be only $41, and profit (41 - 24) = $17. Etc ib eul - e t about different and ca m every at gross m income m and gross mi and delay mi . Suppose that the monopolist gradually lowers the price and sets it at $35. Then he can sell, of course, more than 1 unit of the product, for example, 4 units, but this is also an insignificant amount of sales. At the same time, his gross income will be equal to $140 (35 x 4), and profit (140 - 72) = $68. Following the demand curve, the monopolist, by lowering the price, can increase sales. For example, at a price of $33, he will sell 5 units already. And although the profit per unit of goods will decrease, the total amount of profit will increase. To what extent will the monopolist lower the price in an effort to increase his profit? Obviously, up to the point where marginal revenue (MR) will be equal to the marginal cost (MS) in this case, when selling 9 units of goods.

It is in this case that the amount of profit will be maximum, i.e. (225 - 117) = $ 108. If the seller lowers the price further, for example, to $ 23, then the result will be as follows: having sold 10 units of the product, the monopolist would receive marginal income 5 dollars, and the marginal cost would be 10.5 dollars. Therefore, the sale of 10 units of goods at a price of 23 dollars would lead to a decrease in the profit of the monopolist (230 - 127.5) = 102.5.

Let's return to fig. 7.3. We do not determine the maximum profit margin “by eye”, estimating at what volume of sales the difference between gross income and gross costs is maximum. Marginal revenue and marginal cost determine the slope of the gross revenue and gross cost curves at any point. Let's draw tangents to points L and B. Their equal slope means that MR= MS. It is in this case that the profit of the monopoly will be maximum.

Under conditions of imperfect competition, the equilibrium of the firm (i.e., the equality of marginal cost and marginal revenue, or MS= MR) achieved at such a volume of production, when average costs do not reach their minimum. The price is above the average cost. Perfect competition is equal MS= MR = P-AC. With imperfect competition

(MS = MR)< АС < R(6)

A profit maximizing monopolist always operates on the elastic part of the demand curve, since only when

Rice. 7.5. Monopoly equilibriumin short term

elasticity coefficient greater than one (E D P > 1), marginal revenue is positive. On the elastic part of the demand curve, a price decrease provides the monopolist with an increase in gross income. Let us turn again to the relationship in Fig. 7.3 and 7.4. At E D P=1, marginal revenue is zero, and at E 0 R< 1, marginal revenue becomes negative (see Chapter 5, § 8).

So, the maximum profit can be determined by comparing TR and TS at different volumes of output; the same result will be obtained when compared MR and MS. In other words, the maximum difference between TR and TS(maximum profit) will be observed when the equality MR and MS. Both methods of determining the maximum profit are equivalent and give the same result.

On fig. 7.5 it can be seen that the equilibrium position of the firm is determined by the point £ (the point of intersection MS and MR), from which we draw a vertical to the demand curve D. Thus, we find out the price that provides the greatest profit. This price will be set at E g The shaded rectangle shows the amount of monopoly profit.

Under perfect competition, the firm expands its production without lowering the selling price. Production increases up to the moment of equality MS and mr. The monopolist is guided by the same rule - he compares additional costs and additional income, making a decision to expand, suspend or reduce production, that is, he compares his MS and mr. And he expands production until the moment of equality MS and mr. But the volume of production in this case will be less than it would be under perfect competition, i.e. Q,< Q 2 . При совершенной конкуренции именно in point E 2 marginal cost coincides. (MS) minimum

Chapter 7

Market mechanism of imperfect competition

value of average costs (AU) and selling price level (R). If the price (R 2) set at the point E 2, there would be no monopoly profit.

Price setting by the firm at the point level E 2 would obviously be altruism. At this point MS = AC= R. But at the same time MS > MR. A rationally operating firm will by no means consider it normal that the expansion of production in the name of "public interests" will be accompanied by more additional costs for it than additional income.

Society is interested in a larger volume of production and lower costs per unit of output. With an increase in output from O to Q 2, average costs would decrease, but then, in order to sell additional products, one would either have to lower the price or increase sales promotion costs (and this is due to an increase in marketing costs). This path is not suitable for an imperfect competitor: he does not want to "spoil" his market by lowering prices. To maximize profits, the firm creates a certain deficit, which causes a price that exceeds marginal cost. Scarcity means a limitation (smaller supply) in conditions of imperfect competition compared to its volume, which would be in conditions of perfect competition. This is clear from the graph: in Fig. 7.5 shows that O,< Q 2 .

Monopoly profit in the imperfect competition model is treated as a surplus over normal profit. Monopoly profit is manifested as a result of violation of the conditions of perfect competition, as a manifestation of the monopoly factor in the market.

But how sustainable is this excess over normal profit? Obviously, much will depend on the possibilities for the influx of new firms into the industry. Under perfect competition, higher than normal profits disappear relatively quickly under the influence of an influx of new firms. E With l and same b arriere for entry and I'm in the industry before With exactly you With OK and , t about monopoly pr and true story b re t ae t at st ouch and your character t ep. In the long run, any monopoly is open, so in the long run there is a tendency for monopoly profits to disappear as new producers enter the industry. Graphically, this means that the average cost curve AC will only touch the demand curve. Something similar happens in a market structure called monopolistic competition (see Figure 7.14 below).

To measure the degree of monopoly power in economic theory is used and Lerner index(named after Abba Lerner, an English economist who proposed this indicator in the 30s of the XX century):

L= P-MC_

The greater the gap between P and MC, the greater the degree of monopoly power. Value L is between 0 and 1. Under perfect competition, when P = MS, The Lerner index will naturally be 0.

Perfect competition implies the free flow of all factors of production from industry to industry. Therefore, under conditions of perfect competition, as emphasized by the neoclassical school, there is a clear trend towards zero profit. 1 If there are obstacles to the free flow of resources, there is a monopoly profit.

Considering the marginal income of a monopoly, we said that a decrease in the price of each subsequent unit of goods means a decrease in the price of previous units of production of the monopoly firm. Can an imperfect competitor do the following: sell the first unit of a product at a price of $41, the second at a price of $39, the third at a price of $37, and so on? Then the monopolist would sell each buyer the product at the maximum price he is willing to pay.

So we came to the practice of pricing, which is called price d is Cree mi national and her: selling one and t wow t ovara are different m on t re bit spruce m or gr at ppa m on t re bit firs in different ways m price m , etc and Che m decomp and h and I'm not talking about prices boo caught decomp and h and pits and in and costs for and factory st va. The word "discrimination" here does not mean the infringement of someone's rights, but "separation".

The purpose of the price discrimination policy is to monopolist's desire to appropriate consumer surplus and thereby maximize your profits. Depending on the extent to which he succeeds, price discrimination is divided into three types: discrimination of the first, second and third degree. Let's consider each of these types in detail.

sheet, and the marginal revenue curve

falls off the demand curve for its product

Qiyu (see Figure 7.6). .

Chapter 7

Market mechanism of imperfect competition

Assume that marginal cost is constant. In first-degree price discrimination, the monopolist sells the first unit of good 0 1 at its reserved price. RU the same applies to the second one (sold by Q 2 at a price R 2), and subsequent units. In other words, the maximum of what he is willing to pay is "squeezed" out of each buyer. Then the curve MR coincides with the demand curve D, and the profit-maximizing sales volume corresponds to the point Q n , since it is at the point £ that the marginal cost curve (MS) intersects with the demand curve D(MR) discriminatory monopolist.

Therefore, the marginal revenue from the sale of an additional unit of output in each case will be equal to its price, as in conditions of perfect competition. As a result, the monopolist's profit will increase by an amount equal to consumer surplus (shaded area).

However, such a pricing policy is very rare in practice, since for its implementation, the monopolist must have amazing insight and know exactly what is the maximum price that each buyer is willing to pay for each unit of this product. We can say that perfect price discrimination is the ideal, the "blue dream" of the monopolist. Like any "blue dream", it is extremely rarely achieved. For example, a well-known lawyer, knowing well the solvency of his clientele, can charge each such price for his services, which corresponds to the maximum amount that the client is willing to pay.

Price d is Cree mi national and I am second st epen and is a pricing policy, the essence of which is to set different prices depending on the quantity of purchased products. When buying more goods, the consumer is charged a lower price for each copy of the goods. Another example: in Moscow there are various tariffs

fa for travel on the subway, depending on the number of trips. We can say that the subway implements a policy of price discrimination of the second degree. Very often, second-degree price discrimination takes the form of various price discounts (discounts).

Price d is kr them national and I t re t ey st epen A situation in which a monopolist sells goods to different groups of buyers with different price elasticity of demand. What is happening here is not a division of demand prices into individual copies or volumes of goods, but market segmentation, that is, the division of buyers into groups depending on their purchasing power. The monopolist creates, to put it simply, "expensive" and "cheap" markets.

In the "expensive" market, demand is low elastic, which allows the monopoly to increase revenue by raising prices, and in the "cheap" market it is highly elastic, which makes it possible to increase total revenue by selling more products at lower prices (see Figure 7.7) . The most difficult problem of third-degree price discrimination is to reliably separate one market from another, i.e. "expensive" from "cheap". If this is not done, then the idea of ​​profit maximization will not be realized. After all, consumers in the "cheap" market will buy products at low prices and resell them in the "expensive" market. Let us give a specific example of a fairly reliable division of the market: in a museum of fine arts, tickets for schoolchildren and students are always cheaper than for adult buyers. The museum administration sells cheap tickets only upon presentation of an appropriate certificate, and visually verifying the age of the buyer. Imagine a situation where enterprising schoolchildren would buy lots of cheap tickets and then resell them at the entrance to adult visitors at prices lower than those set by the museum for

Chapter 7

Market mechanism of imperfect competition

adults is impossible. After all, even if an elderly art lover uses the services of a young businessman, at the control entrance he will have to present not only a cheap ticket, but also his blooming youthful appearance.

A clear example of third-degree price discrimination can be seen in the famous novel by I. Ilf and E. Petrov “The Twelve Chairs”, when Ostap Bender was selling tickets overlooking the “Proval”: “Get tickets, citizens! Ten cents! Children and Red Army soldiers for free. Students five kopecks! Non-union members - thirty kopecks!” Third-degree price discrimination is also carried out when setting different prices for hotel services to foreign and domestic visitors, different prices for dishes in a restaurant during the day and in the evening, etc.

Let us explain the idea of ​​price discrimination of the third degree graphically. On fig. 7.7 the markets on which the discriminating monopolist operates are shown: cases and and b. Let's assume that the marginal cost MS are the same when selling products at different prices. Curve intersection MS and MR determines the price level. Since the price elasticity in the "expensive" and "cheap" markets is different, their prices will also be different as a result of price discrimination. In the "expensive" market, the monopolist will set the price P, and the volume of sales will be Q,. In the "cheap" market, the price will be at the level R 2 and sales volume Q 2 . Gross income in all cases is shown as shaded boxes. The sum of the areas of the rectangles in cases a) and b) will be higher than the area denoting the gross income of a monopolist that does not conduct price discrimination (case c).

Thus, a discriminating monopolist must be able to reliably divide its market, focusing on different price elasticity of demand for different consumers.

Conditions for profit maximization under perfect competition.

ANSWER

According to the traditional theory of the firm and the theory of markets, profit maximization is the main goal of the firm. Therefore, the firm must choose such a volume of supplied products in order to achieve maximum profit for each period of sales.

PROFIT is the difference between gross (total) income (TR) and total (gross, total) production costs (TC) for the sales period:

profit = TR - TS.

Gross income- this is the price (P) of the goods sold, multiplied by the volume of sales (Q).

Since the price is not affected by a competitive firm, it can affect its income only by changing the volume of sales. If the firm's gross income is greater than its total costs, then it makes a profit. If the total cost exceeds the gross income, then the firm incurs losses.

total costs is the cost of all factors of production used by the firm in the production of a given volume of output.

Maximum Profit achieved in two cases:

a) when the gross income (TR) exceeds the total costs (TC) to the greatest extent;

b) when marginal revenue (MR) is equal to marginal cost (MC).

Marginal Revenue (MR) is the change in gross income resulting from the sale of an additional unit of output. For a competitive firm, marginal revenue is always equal to the price of the product:

The marginal profit maximization is the difference between the marginal revenue from the sale of an additional unit of output and the marginal cost:

marginal profit = MR - MC.

marginal cost Additional costs that increase output by one unit of the good. Marginal cost is entirely variables costs because fixed costs do not change with output. For a competitive firm, marginal cost is equal to the market price of the good:

The marginal condition for profit maximization is the level of output at which price equals marginal cost.

Having determined the profit maximization limit of the firm, it is necessary to establish an equilibrium output that maximizes profit.

The most profitable equilibrium This is the position of the firm in which the volume of goods offered is determined by the equality of the market price to marginal cost and marginal revenue:

The most profitable equilibrium under perfect competition is illustrated in Fig. 26.1.

Rice. 26.1. Equilibrium output of a competitive firm

The firm chooses the volume of output that allows it to extract the maximum profit. At the same time, it should be borne in mind that the output that provides the maximum profit does not mean at all that the largest profit is extracted per unit of this product. It follows that it is wrong to use unit profit as a measure of total profit.

In determining the level of output that maximizes profit, it is necessary to compare market prices with average costs.

Average cost (AC)- costs per unit of output; equal to the total cost of producing a given quantity of output divided by the quantity of output produced. Distinguish three type of average costs: average gross (total) costs (AC); average fixed costs (AFC); average variable costs (AVC).

The ratio of market price and average production costs can have several options:

The price is greater than the average cost of production, maximizing profit. In this case, the firm extracts economic profit, i.e., its income exceeds all its costs (Fig. 26.2);

Rice. 26.2. Profit maximization by a competitive firm

The price is equal to the minimum average production costs, which provides the company with self-sufficiency, i.e., the company only covers its costs, which makes it possible for it to receive a normal profit (Fig. 26.3);

Rice. 26.3. Self-sustaining competitive firm

The price is below the minimum possible average cost, that is, the firm does not cover all its costs and incurs losses (Fig. 26.4);

The price falls below the minimum average cost, but exceeds the average minimum variables costs, i.e. the firm is able to minimize its losses (Fig. 26.5); price below average low variables costs, which means the cessation of production, because the company's losses exceed fixed costs (Fig. 26.6).

Rice. 26.4. Competitive firm incurring losses

Rice. 26.5. Minimizing the losses of a competitive firm

Rice. 26.6. Termination of production by a competitive firm

author Utkina Svetlana Anatolievna

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Since the monopolist is the only producer of a given good, the demand curve for the monopolist's product is at the same time the market demand curve for the good. This curve has, as usual, a negative slope (Fig. 11.16). Therefore, the monopolist can control the price of his product, but then he will have to face a change in the magnitude of demand: the higher the price, the lower the demand. Monopoly is a price finder. Its goal is to set a price (respectively, choose such an issue) at which its profit will be maximum.

The general rule is that profit is maximized at the output when marginal revenue equals marginal cost - MR = MS(topic 10, paragraph 10.3) - remains true for a monopoly. The only difference is that for a perfectly competitive firm, the marginal revenue line (MR) is horizontal and coincides with the market price line at which this firm can sell any quantity of its products (topic 10, paragraph 10.2). In other words, the marginal revenue of a competitive firm is equal to price. On the contrary, for the monopoly line MR is not horizontal and does not coincide with the price line (demand curve).

To justify this, remember that marginal revenue is the increment in revenue when output is increased by one unit:

For an example of calculating marginal revenue, take

the simplest demand function for a monopoly product: P= 10 - q. Let's make a table (Table 11.1).

Table 11.1. Marginal revenue of a monopolist

TR (P X q)
MR (ATR/Aq)	9 7 5 3 1 -1 -3 -5 -7 -9

It follows from the data in the table that if the monopolist reduces the price from 10 to 9, demand increases from 0 to 1. Accordingly, revenue increases by 9. This is the marginal revenue received from the release of an additional unit of output. An increase in output by one more unit leads to an increase in revenue by another 7, and so on. In the table, the values ​​of marginal revenue are located not strictly under the values ​​of price and demand, but between them. In this case, the output increments are not infinitesimal, and therefore the marginal revenue is obtained, as it were, “on the transition” from one production quantity to another.

At the moment when marginal revenue reaches zero (the last unit of output does not increase revenue at all), the revenue of the monopoly reaches a maximum. A further increase in production leads to a drop in revenue, i.e. marginal revenue becomes negative.

The data in the table allow us to conclude that the value of marginal revenue related to each output value (except zero) is less than the corresponding price value. The fact is that when an additional unit of output is produced, revenue increases by the price of this unit of output ( R). At the same time to sell this extra unit

output, it is necessary to reduce the price by the value But according to the new

price, not only the last, but also all previous units of the issue are sold (q), previously sold at a higher price. Therefore, the monopolist suffers a loss in revenue from the price reduction,

equal . Subtracting from the gain from output growth the loss from

price reduction, we obtain the value of marginal revenue, which is, therefore, less than the new price:

With infinitesimal changes in price and demand, the formula takes the form:

where is the derivative of the price function with respect to demand.

Let's return to the table. Let the monopolist set a price of 7 last week by selling 3 units at it. goods. In an attempt to increase revenue, he lowers the price to 6 this week, allowing him to sell 4 units. goods. Hence, from the expansion of output by one unit, the monopolist receives 6 units. additional income. But from the sale of the first 3 units. of goods, he now receives only 18 units. revenue instead of 21 units. last week. The losses of the monopolist from the price reduction are, therefore, 3. Therefore, the marginal income from the expansion of sales with the price reduction is: 6 - 3 = 3 (see Table 11.1).

It can be rigorously proven that with a linear demand function for the monopolist's product, the function of its marginal revenue is also linear, and its slope is twice the slope of the demand curve(Fig. 11.3).

If the demand function is given analytically: R = P(q), then to determine the marginal revenue function, it is easiest to first calculate

Rice. 11.3.

maintain the output revenue function: TR = P(q)xq, and then take its output derivative:

Let's combine the functions of demand, marginal revenue (MR) marginal (MS) and average costs (AU) monopolist in one figure (Fig. 11.4).

Rice. 11.4.

Point of intersection of curves MR and MS defines release (q m), at which the monopolist earns the maximum profit. Marginal revenue is equal to marginal cost. On the demand curve, we find the monopoly price corresponding to this output (P t). At this price (output) the monopoly is in a state of equilibrium for it is unprofitable for her to raise or lower the price.

In this case, at the equilibrium point, the monopolist receives economic profit (surplus profit). It is equal to the difference between its revenue and total costs:

On fig. 11.4 revenue is the area of ​​the rectangle OP m Eq m , total cost - area of ​​rectangle OCFq m . Therefore, the profit is equal to the area of ​​the rectangle CP m EF.

It is noteworthy that in conditions of monopoly equilibrium, the price is higher than marginal cost. This is different from the equilibrium of a competitive firm: such a firm chooses an output at which price exactly equals marginal cost. The problems arising from this will be discussed below.

In the topic “Perfect competition” (item 4), it was said that in the long run a competitive firm is not able to earn economic profit. This is not the case in a monopoly. As soon as the monopolist manages to protect its market from the invasion of competitors, it maintains economic profit in the long run.

At the same time, the possession of monopoly power does not in itself guarantee economic profit, even in the short run. A monopolist can incur losses if the demand for its products falls or its costs increase - for example, due to an increase in resource prices or taxes (Fig. 11.5).

Rice. 11.5.

In the figure, the monopoly's average total cost curve is above the demand curve for any output, which condemns the monopoly to losses. By choosing an output at which marginal revenue equals marginal cost, the monopolist minimizes its losses in the short run. The total loss in this case is equal to the area CFEPm. In the long run, the monopolist may try to lower its costs by changing the amount of capital employed. In case of failure, he will have to leave the industry.